Conquering the Integral of (1/x)*exp(-ax^2): A Scientific Inquiry

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Homework Help Overview

The discussion revolves around the integral of the function (1/x)*exp(-ax^2), exploring its properties and potential solutions. Participants are examining the mathematical challenges associated with this integral, particularly in the context of expectation values and function behavior.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of Taylor expansion and express frustration with the resulting complexities. There are mentions of using computational tools like WolframAlpha, which suggests the involvement of special functions. Questions arise regarding the feasibility of solving the integral by hand and the implications of the expectation value being infinite.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and reflections on the problem. Some have acknowledged the challenges posed by the integral and the implications of its properties, while others are questioning the assumptions related to the function's behavior.

Contextual Notes

There is a mention of the function 1/x being odd, which raises questions about its integral and the implications for the expectation value. The discussion hints at the complexities introduced by the nature of the function and the limits of integration.

GrandsonOfMagnusCarl
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Homework Statement
Essentially - find <1/x>, i.e. the mean of 1/x. The distribution probability density is of the form exp(-ax^2).
Relevant Equations
Mean of G = integrate ( G f(x) ) dx
Hopeless. I tried to use Taylor expansion but the zeroes and infinities go out of control really quick.
I tried WolframAlpha and it gave a special function.
What integrating trick am I missing? Or is it nonsense to solve it simply by hand?
 
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The expectation value is infinite.
 
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Orodruin said:
The expectation value is infinite.
Ah I'm so stupid. Thank you. Also another reality check for me.
 
<1/x>=0 as 1/x is an odd function and G*f(x) is then also odd.
 

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